This simplest way to reduce the brightness given the existing circuit is to reduce the high voltage. The brightness will be non-linear with that voltage, but you should be able to find a point that has the brightness you want without it being too dependent on small changes in the high voltage.
The high voltage is generated by a boost converter run by a
666 555 timer:
It looks like when the voltage gets high enough, T12 is turned on, which kills the oscillations. That's pretty crude, will have a strong temperature dependency, and will be touchy to adjust. However, P2 is already there for the purpose of adjusting the high voltage. The more you turn the wiper to the R4 end, the lower the high voltage.
If the existing adjustment range doesn't allow the brightness to get low enough, make R3 a little bigger and/or R4 a little smaller.
If the adjustment is too finicky, put a zener diode in series with the base of T12 and add maybe a 1 MΩ resistor to ground right on the base of T12. That will change the setting range of the high voltage significantly, so R3 and R4 need to be adjusted accordingly. Make sure that the maximum voltage the tubes, D5, and T1 can handle can't ever be attained no matter how P2 is set.